Matlab 2016b: Determine unassigned symbolic functions of an expression

Question

how can I determine unassigned symbolic functions (syms f(t)) of an expression. Excluding symbolic math functions (sin,...) and symbolic variables (syms a).

For example:

syms a(t) b(t) c
expr = a(t)*diff(b, t) + c*diff(a,t)^2 + sin(c*pi)*cos(b);

examining symbolic variables

>> symvar(expr)
[ c, t]

and how to do it for unassigned symbolic functions

>> XXXXX(expr)
[ a(t), b(t), diff(a, t), diff(b, t)]
% or
[ a(t), b(t)]
% or
[ a, b]

Answer 1

For MATLAB 2019a and newer

>> X = findSymType(expr,'symfun')

X =

[ a(t), b(t)]

From the documentation:

Find an unassigned symbolic function of type 'symfun' in the equation.

For previous MATLAB versions, I don't see such a function. Only option I see is to write a function yourself.

>> feval(symengine,'type',expr)

ans =

_plus

>> feval(symengine,'type',b(t))

ans =

function

>> feval(symengine,'type',sin(t))

ans =

sin

The mupad type function allows you to identify the type of an expression, you are looking for "function". Here is some code, which looks for all terms of a certain type:

function z=mst(x,symtype)
y=children(x);
if strcmpi(char(feval(symengine,'type',x)),symtype)
    z=x;
else
    z=[];
end
if ~isequal(x,y)
for ix=1:numel(y)
   z=[z;mst(y(ix),symtype)];
end
end
end

an example call:

>> mst(expr,'function')

ans =

 b(t)
 a(t)
 a(t)
 b(t)